Hecke Correspondence for Automorphic Integrals with Infinite Log-Polynomial Periods
type: CreativeWork
description: Since Hecke first proved his correspondence between Dirichlet series with functional equations and automorphic forms, there have been a great number of generalizations. Of particular interest is a generalization due to Bochner that gives a correspondence between Dirichlet series with any finite number of poles that satisfy the classical functional equation and automorphic integrals with (finite) log-polynomial sum period functions. In this dissertation, we extend Bochner's result to Dirichlet series with finitely many essential singularities. With some restrictions on the underlying group and the weight, we also prove a correspondence for Dirichlet series with infinitely many poles. For this second correspondence, we provide a technique to approximate automorphic integrals with infinite log-polynomial sum period functions by automorphic integrals with finite log-polynomial period functions.
abstract: Since Hecke first proved his correspondence between Dirichlet series with functional equations and automorphic forms, there have been a great number of generalizations. Of particular interest is a generalization due to Bochner that gives a correspondence between Dirichlet series with any finite number of poles that satisfy the classical functional equation and automorphic integrals with (finite) log-polynomial sum period functions. In this dissertation, we extend Bochner's result to Dirichlet series with finitely many essential singularities. With some restrictions on the underlying group and the weight, we also prove a correspondence for Dirichlet series with infinitely many poles. For this second correspondence, we provide a technique to approximate automorphic integrals with infinite log-polynomial sum period functions by automorphic integrals with finite log-polynomial period functions.
author: Daughton, Austin James Chinault
language: eng
keywords: Mathematics, Automorphic Forms, Automorphic Integrals, Hecke Correspondence, Number Theory
license: http://rightsstatements.org/vocab/InC/1.0/
date published: 2012
date modified: 2026-07-27T21:21:14Z
provider: Temple University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Temple University. Libraries

PropertyValue
property ID: Handle
value: http://hdl.handle.net/20.500.12613/1054